"I am always confident of holding on to players, but if you want me to sit here and guarantee that he (Cole) will be an Arsenal player next season I cannot do it," Wenger was quoted as saying by Daily Mirror newspaper on Wednesday.
"He only has two years left on his contract and we have not made any movement in that regard and when you have a player in that situation you cannot say much."
Cole has been linked with a move to London rivals Chelsea since found guilty of an illegal approach to the English champions last season.
The England international has also criticized Arsenal in his autobiography for using him as a "scapegoat" in the tapping-up row with Chelsea.
But Wenger insisted Arsenal are yet to receive any offer for the services of the 25-year-old international.
"There is nothing going on with Ashley at the moment. There is no offer and we are not talking to anybody about him," the French coach said.
Chelsea are looking for a new left-back after Spanish international Asier Del Horno joined Valencia.